Better than the chance of the peasantry, to say the least. I did some research on this a little while back, and came across a secion in Medieval Children by Nicholas Orme where he talks about this.

Quoting from the relevant section of the book:

Not all the children survived to grow up. [Subtracting infant deaths] it produced an average number of only just over four children per monarch, six if we include the infants who died. This average four was sometimes depleted by further deaths in childhood. [...]

Once we leave the royal family, [...][Dr. J.S. Moore's work] suggests that the average size of baronial families was between 4.15 and 4.83, and of knightly ones between 4.55 and 5.71. These figures include the parents, which leaves the average number of children somewhere between two and three. On either side of these averages, there might be a range in the number from one to ten, perhaps more. The data on which such figures are based, however, are likely to ignore children who died in infancy, and come from 'snapshots' of families at particular dates. Taking infant mortality into account, the total number of children born to baronial and knightly parents is likely to have been higher, as it was in the royal family.

[...] Studies of rural society between the 12th and mid-14th centuries suggest that, in poor labouring families, the average number of children was slightly less than two. Among peasants who farmed their own holdings, the survival rate was better, rising to as many as five in the wealthiest families.

So the take away here is that a Royal parent would have six children, give or take, and two would die in infancy. The lower down in social standing we go, the less records we have, so there simply aren't mentions of infants dying, but we at least know how many survived to be mentioned in the records.